$\displaystyle \text{In cylindrical coordinates: }\;\theta\:=\: \frac{\pi}{3}$

$\displaystyle \text{I must take it into cartesian coordinates and graph.}$

$\displaystyle \text{I've tried this way:}$

$\displaystyle \begin{Bmatrix}x&=&r\cos\frac{\pi}{3}\\ \\[-3mm] y&=&r\sin\frac{\pi}{3} \\ \\[-3mm] z&=&z\end{matrix}\quad\Rightarrow\quad \begin{Bmatrix}x&=& \frac{1}{2}r & [1] \\ \\[-3mm] y&=&{\frac{\sqrt{3}}{2}\,\!r & [2] \\ \\[-3mm] z&=&z\end{matrix}}$

$\displaystyle \text{I think its a semi-plane parallel to the line: }\:\frac{2}{\sqrt{3}}y-2x\:=\:0$

Um, it's the entire plane . . .